Heat the oil in a large pan over medium-high heat. Add onion and cook until softened, about 2-3 minutes.
Add garlic and spinach to the pan and cook until spinach just starts to wilt. Season with salt and pepper then remove from heat to cool.
Butterfly the turkey by slicing horizontally into the long, thick side of the breast, being careful not to slice all the way through. Open the turkey to lay flat and place, cut side up, on a piece of plastic wrap.
Using a meat mallet or rolling pin, flatten until ¼ inch thick. Remove plastic wrap.
Arrange ½ the spinach mixture, brie slices and apricot over the turkey, leaving a 2 cm border. Press evenly to flatten.
Starting with one long edge, tightly roll the turkey into a log and tie tightly with kitchen string.
Transfer the turkey, seam side down, to the prepared baking sheet. Bake until a thermometer inserted in the center reads 160 degrees, about 1hr 15m.
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